Hello,

I have a problem of needing to perform an operation on a vector which results in each element being inverted. i.e.

f(x) =y, where

x= [x1 x2 ... xN] andy= [1/x1 1/x2 ... 1/xN]

I'd really appreciate all of your help!

Fran

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- Oct 31st 2009, 06:04 AMfp04Element-wise vector inversion
Hello,

I have a problem of needing to perform an operation on a vector which results in each element being inverted. i.e.

f(**x**) =**y**, where

**x**= [x1 x2 ... xN] and**y**= [1/x1 1/x2 ... 1/xN]

I'd really appreciate all of your help!

Fran - Oct 31st 2009, 06:08 AMtonio
- Oct 31st 2009, 06:32 AMfp04
Sorry, maybe I wasn't clear. Let me give you the entire problem I'm solving....

I work in the field of MRI Physics. I need to perform the following optimisation:

min{m1,m2} l2norm(Fm1 - y1) + l2norm(Fm2 - y2) + lambda* l1norm(f(m1,m2))

F is the Fourier matrix, m1 and m2 are vectors of length of 512^2, y1 and y2 are vectors of the same length and lambda is a normalisation constant.

The function f divides vectors m1 and m2 in an elementwise manner.

As the vectors are so large I would like to use a conjugate gradient method to perform the optimisation. Therefore, I need to take the derivative of the function w.r.t m1 and m2. However, the elementwise division of m1 and m2 is undifferentiable.

So, I need to rewrite the elementwise division of two vectors in a way which is differentiable. Therein lies the problem!

Is this clear...? - Oct 31st 2009, 07:16 AMtonio